What is the derivative of ((x-1)(x-3))/((x-2)^2) ?

The derivative of ((x-1)(x-3))/((x-2)^2) is 2/((x-2)^3)

What is the first derivative of ((x-1)(x-3))/((x-2)^2) ?

The first derivative of ((x-1)(x-3))/((x-2)^2) is 2/((x-2)^3)

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derivative of

\frac{( x - 1 ) ( x - 3 )}{( x - 2 ) ^{2}}

\frac{2}{( x - 2 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{( x - 1 ) ( x - 3 )}{( x - 2 ) ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ( x - 1 ) ( x - 3 ) ) ( x - 2 ) ^{2} - \frac{d}{d x} ( ( x - 2 ) ^{2} ) ( x - 1 ) ( x - 3 )}{( ( x - 2 ) ^{2} ) ^{2}}

\frac{d}{d x} ((x - 1) (x - 3)) = 2 x - 4

\frac{d}{d x} ((x - 2)^{2}) = 2 (x - 2)

= \frac{( 2 x - 4 ) ( x - 2 ) ^{2} - 2 ( x - 2 ) ( x - 1 ) ( x - 3 )}{( ( x - 2 ) ^{2} ) ^{2}}

Simplify

\frac{( 2 x - 4 ) ( x - 2 ) ^{2} - 2 ( x - 2 ) ( x - 1 ) ( x - 3 )}{( ( x - 2 ) ^{2} ) ^{2}} : \frac{2}{( x - 2 ) ^{3}}

= \frac{2}{( x - 2 ) ^{3}}

1 + sin^{2} (x)

2 e^{3} x

y = 2 x^{5}

\frac{d}{d a} (5 tan^{2} (a) - 5 sec^{2} (a) + 1)

\frac{d}{d x} (x^{2} + (p - 2) \cdot x + 2 (8 - p))

What is the derivative of ((x-1)(x-3))/((x-2)^2) ?
The derivative of ((x-1)(x-3))/((x-2)^2) is 2/((x-2)^3)
What is the first derivative of ((x-1)(x-3))/((x-2)^2) ?
The first derivative of ((x-1)(x-3))/((x-2)^2) is 2/((x-2)^3)